Journal
DUKE MATHEMATICAL JOURNAL
Volume 167, Issue 7, Pages 1347-1432Publisher
DUKE UNIV PRESS
DOI: 10.1215/00127094-2017-0055
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Funding
- National Science Foundation (NSF) [DMS-1361856, DMS-1700261]
- Russian Science Foundation (RSF) [17-11-01126]
- CNRS/Projet International de Cooperation Scientifique (PICS) project Isomonodromic Deformations and Conformal Field Theory
- NSF [DMS-1361856, DMS-1700261, DMS-1637087]
- RSF [17-11-01126]
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We discuss an extension of the Jimbo-Miwa-Ueno differential 1-form to a form closed on the full space of extended monodromy data of systems of linear ordinary differential equations with rational coefficients. This extension is based on the results of M. Bertola, generalizing a previous construction by B. Malgrange. We show how this 1-form can be used to solve a long-standing problem of evaluation of the connection formulae for the isomonodromic tau functions which would include an explicit computation of the relevant constant factors. We explain how this scheme works for Fuchsian systems and, in particular, calculate the connection constant for the generic Painleve VI tau function. The result proves the conjectural formula for this constant proposed by Iorgov, Lisovyy, and Tykhyy. We also apply the method to non-Fuchsian systems and evaluate constant factors in the asymptotics of the Painleve II tau function.
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